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ZIMSEC O Level · 4030/1 · N2017

Mathematics Paper 1 November 2017 (topical set)

Questions
53
Total marks
109
Time allowed
150 min
Syllabus code
4030/1

These questions are attributed to this sitting but were printed in a topical collection, so this is not the whole paper as it was sat.

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Questions
53
Pass mark
32
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 2

[3 marks]Rational, Irrational Numbers & Surds
From the following list of numbers write down the rational numbers: 3.1 ; sqrt(3) ; pi ; 0.3 ; sqrt(169) ; 17/19

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Question 3

[3 marks]Laws of Indices
Simplify (a) (2 + x)^0, (b) 3x^-2/(3x).

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Question 4

[3 marks]Polygons, Symmetry & Circles
(a) Write down the special name given to triangle ABC. [1] (b) Calculate the angles marked (i) p, [1] (ii) q. [1]

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Question 7

[3 marks]Fractions, Decimals & Percentages
Evaluate, giving your answer in its lowest terms, (a) 4/5 - 9/10, (b) 7/15 x 3/8 ÷ 7/8.

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Question 8

[3 marks]Ratios, Rates & Proportions
(a) Express the ratio 3,5 : 1 in the form a : b where a and b are integers. [1] (b) Shuvai mixed hot water and cold water in the ratio 3,5 : 1 to get warm water. If she ended up with 45 litres of warm water, calculate the amount of hot water she used. [2]

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Question 9

[3 marks]Statistics & Probability
The mean of 9 numbers is 11,9. The mean of 8 of the numbers is 13. Find the ninth number.

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Question 10

[3 marks]Quadratic Equations
Solve the equation 3x^2 - 5x - 2 = 0.

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Question 14

[3 marks]Measures & Mensuration
In the diagram, PQRS is a trapezium with PQ parallel to SR, PQ = 5 cm, PS = 8 cm, SR = 11 cm and angle PSR = 30 degrees. Calculate the area of the trapezium. [Use as much of the information given below as is necessary]. [sin 30 = 0,500; cos 30 = 0,866; tan 30 = 0,577]

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Question 20

[4 marks]Number Bases
(a) Convert 1001_2 to a number in base 6. [2] (b) Given that 111_n = 73_10, find the value of n. [2]

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Question 101

[1 marks]Approximations & Estimations
Express 99.987 correct to one decimal place.

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Question 102

[1 marks]Approximations & Estimations
Express 99.987 correct to one significant figure.

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Question 103

[1 marks]Ordinary & Standard Form
Express 99,987 in standard form.

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Question 501

[2 marks]Change of Units
Calculate the number of minutes between 1935 and midnight of the same day.

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Question 502

[1 marks]Fractions, Decimals & Percentages
Write 75% as a common fraction in its lowest terms.

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Question 601

[2 marks]Approximations & Estimations
Estimate the value of (7,63 x 5,81 x 9,3)/(27,1 x 31,2) by rounding off each number correct to one significant figure.

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Question 602

[1 marks]Factorisation, H.C.F & L.C.M
Find the Highest Common Factor (H.C.F) of 9 and 12.

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Question 1101

[1 marks]Fractions, Decimals & Percentages
Find the square of 1/4.

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Question 1102

[2 marks]Consumer Arithmetic
Calculate the rate at which 500earns500 earns 320 simple interest in 4 years. [2]

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Question 1201

[3 marks]Sets
It is given that the universal set xi = {x: 10 <= x < 20, x is an integer}, subset A = {x: x is a prime number}, subset B = {x: x is a factor of 3} and subset C = {x: x is an odd number}. Write down the largest element of subset A.

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Question 1202

[3 marks]Sets
It is given that xi = {x: 10 <= x < 20, x is an integer} and subset B = {x: x is a factor of 3}. Find n(B).

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Question 1203

[3 marks]Sets
It is given that xi = {x: 10 <= x < 20, x is an integer}, subset A = {x: x is a prime number} and subset C = {x: x is an odd number}. List elements of A intersect C.

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Question 1301

[2 marks]Approximations & Estimations
It is given that the length, l, of a side of a square is 7 cm, measured to the nearest centimetre. Write the range in which the length of the side of the square must lie, giving your answer in the form a <= l < b where a and b are to be found.

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Question 1302

[1 marks]Approximations & Estimations
It is given that the length, l, of a side of a square is 7 cm, measured to the nearest centimetre. Calculate the least possible perimeter of the square.

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Question 1501

[1 marks]Polygons, Symmetry & Circles
What is the number of lines of symmetry on a general parallelogram?

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Question 1502

[2 marks]Ordinary & Standard Form
Find the exact value of 4mn when m = 4 x 10^4 and n = 5 x 10^-9, giving the answer as a decimal.

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Question 1601

[1 marks]Matrices
Given that matrix T = (3 -6; 4 1), find the determinant of matrix T.

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Question 1602

[2 marks]Vector Geometry
If n = (-3; 9) find |n|, giving the answer in surd form. [2]

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Question 1701

[1 marks]Substitution
Given that d = 2n - 1, find d when n = 8.

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Question 1702

[2 marks]Scales & Simple Map Problems
On a map of scale 1 : 50 000, a stream is 7 cm long. Calculate the actual length of the stream, giving the answer in km.

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Question 1801

[1 marks]Trigonometry, Bearing & Distances
Write down the three-figure bearing equivalent to the direction North West.

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Question 1802

[3 marks]Polygons, Symmetry & Circles
The diagram shows a regular polygon with angles marked x and y. Calculate the value of (i) x, [2] (ii) y. [1]

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Question 1901

[2 marks]Inequalities
Solve the inequality 3x + 1 < 28 <= 5x - 2.

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Question 1902

[1 marks]Inequalities
Find the number of integers which satisfy the inequality 3x + 1 < 28 <= 5x - 2.

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Question 1903

[1 marks]Inequalities
If x is an odd integer, write down its least value which satisfies the inequality 3x + 1 < 28 <= 5x - 2.

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Question 2101

[2 marks]Circle Geometry
In the diagram, the points A, B and C are on the circumference of a circle centre O. angle OBA = 30. Calculate angle AOB.

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Question 2102

[2 marks]Circle Geometry
In the diagram, the points A, B and C are on the circumference of a circle centre O. angle OBA = 30. Calculate angle ACB.

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Question 2201

[2 marks]Geometrical Transformation
Matrix R = (3 0; 0 1). R represents a transformation that maps point P(x; y) onto P1(3; 4). Calculate the value of x and the value of y.

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Question 2301

[2 marks]Factorisation, H.C.F & L.C.M
Factorise completely the expression 4x^2 - y^2.

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Question 2302

[3 marks]Quadratic Equations
Given that 2x + y = 10, solve the equations 4x^2 - y^2 = 40 and 2x + y = 10.

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Question 2401

[2 marks]Trigonometry, Bearing & Distances
In the diagram angle PQR = 90 degrees, PQ = 5 cm and angle QPR = 60 degrees. Calculate PR. (sin 60 = 0,866; cos 60 = 0,500; tan 60 = 1,732)

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Question 2402

[3 marks]Linear Equations
Solve the equations (i) 0,2n = 5, (ii) (1/3)m + 2 = 8.

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Question 2501

[2 marks]Travel Graphs
The graph shows part of a velocity-time graph of a moving object. The object travels at a constant velocity of V m/s for 10 seconds. It then accelerates uniformly until it reaches a velocity of 15 m/s in 4 seconds. The distance travelled during the first 10 seconds is 50 m. Calculate V.

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Question 2601

[1 marks]Similarity & Congruency
The diagram shows two triangles PQR and RST such that PQ is parallel to ST, PQ = 3 cm, ST = 8 cm and RT = 12 cm. PRT and QRS are straight lines. Name the triangle similar to triangle PQR.

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Question 2602

[2 marks]Similarity & Congruency
Two triangles PQR and RST have PQ parallel to ST, PQ = 3 cm, ST = 8 cm and RT = 12 cm, with PRT and QRS straight lines. Calculate PR.

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Question 2701

[2 marks]Change of Subject of Formula
When a rod of length l cm is heated to a temperature of t degrees C, it expands. Its new length, x cm, is given by the formula x = l + alt. Make a the subject of the formula.

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Question 2702

[2 marks]Change of Subject of Formula
Using x = l + alt, find x when l = 2 cm, a = 0,01 and t = 50 degrees C.

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Question 2703

[2 marks]Change of Subject of Formula
Using x = l + alt, find a when x = 3,1 cm, l = 3 cm and t = 40 degrees C.

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Question 220201

[1 marks]Substitution
Given that r = 27, s = 1/3 and t = 2, find the value of r^s.

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Question 220202

[2 marks]Substitution
Given that r = 27, s = 1/3 and t = 2, find the value of s^(-t).

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Question 250201

[2 marks]Travel Graphs
The graph shows part of a velocity-time graph of a moving object. The object travels at a constant velocity of V m/s for 10 seconds. It then accelerates uniformly until it reaches a velocity of 15 m/s in 4 seconds. Find the acceleration during the last 4 seconds.

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Question 250202

[2 marks]Travel Graphs
The graph shows part of a velocity-time graph of a moving object. The object travels at a constant velocity of V m/s for 10 seconds. It then accelerates uniformly until it reaches a velocity of 15 m/s in 4 seconds. Find the total distance travelled by the object in the 14 seconds.

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Question 260301

[3 marks]Similarity & Congruency
Triangle RQP is mapped onto triangle RST by a transformation A. Describe fully transformation A, given that PQ is parallel to ST, PQ = 3 cm, ST = 8 cm and PRT and QRS are straight lines.

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Question 260302

[3 marks]Geometrical Transformation
In the diagram, PT and QS are straight lines that cross at R. PQ = 3, ST = 8 and RT = 12. Triangle RQP is mapped onto triangle RST by a transformation A. Describe fully transformation A.

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